名校
解题方法
1 . 已知椭圆
的离心率为
,且椭圆过点
.
(1)求椭圆
的标准方程;
(2)过右焦点
的直线
与椭圆
交于
两点,线段
的垂直平分线交直线
于点
,交直线
于点
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f01cdd4ed5c7db717c483f779d90576b.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过右焦点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/639c3d2ff5ee566fcc1b69c65712a661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cff8d039dd1991c12d2de58d1dc2937a.png)
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2022-05-24更新
|
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5卷引用:天津市第二十五中学2022-2023学年高二上学期期中数学试题
天津市第二十五中学2022-2023学年高二上学期期中数学试题天津市和平区2022届高三下学期三模数学试题(已下线)专题6 圆锥曲线硬解定理 微点2 圆锥曲线硬解定理综合训练(已下线)重难点12五种椭圆解题方法-1北京市中国人民大学附属中学2023届高三上学期数学统练四试题
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2 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49ece1ff6ef30715270707ff217acfb7.png)
(1)若
,求函数f(x)在点(1,f(1))处的切线方程;
(2)当
时,讨论f(x)的单调性;
(3)设f(x)存在两个极值点
且
,若
求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49ece1ff6ef30715270707ff217acfb7.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
(3)设f(x)存在两个极值点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a42526840a0fc525571737bed3d1af6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/378b70fac915f3ad6ab0c510a67c8fa6.png)
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4卷引用:天津市蓟州区第一中学、宁河区芦台第一中学等五校2021-2022学年高二下学期期中联考数学试题
名校
解题方法
3 . 已知椭圆
的两个顶点分别为
,
,焦点在
轴上,离心率为
.
(1)求椭圆
的方程;
(2)若直线
与
轴交于点
,与椭圆
交于
,
两点,线段
的垂直平分线与
轴交于
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/913f78382630e50543e5f7192cae3ed3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c850811ba59a05e945a665196539a048.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca0bc80d700368fb8abd76d8f1652a5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36ca989fde677d756f43ae80be053e2a.png)
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2022-03-10更新
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8卷引用:天津市九十六中学2022-2023学年高二上学期期末数学试题
天津市九十六中学2022-2023学年高二上学期期末数学试题天津市区重点中学2022届高三下学期一模联考数学试题福建省连城县第一中学2022-2023学年高二上学期第二次月考数学试题安徽省淮北市树人高级中学2023-2024学年高二上学期第一次阶段考试数学试题(已下线)第三章 圆锥曲线单元测试(基础版)-【冲刺满分】2023-2024学年高二数学重难点突破+分层训练同步精讲练(人教A版2019选择性必修第一册)(已下线)专题29 圆锥曲线中的最值、范围问题- 2022届高考数学一模试题分类汇编(新高考卷)(已下线)数学-2022年高考押题预测卷01(北京卷)重庆市万州第二高级中学2024届高三上学期7月月考数学试题
名校
4 . 已知函数
,
.
(1)讨论
的单调区间;
(2)当
时,令
.
①证明:当
时,
;
②若数列
满足
,
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eeea9bb195a844feb2f1806db8259604.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3ee7c7dd3a775fa701366908859c614.png)
①证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fd791cdf876b9a9e58f251f803aeb66.png)
②若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d6f4a302d3a9023c0a82b889f4ba918.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e92903b4ad4fc018c9f7d0309ed20403.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63554d67f64c68adbd28bce22fb79b28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e7378e6e95cfe560f97ec0e7951e15a.png)
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9卷引用:天津市第四十七中学2023-2024学年高二下学期第二次阶段性检测(6月)数学试题
2022高三·全国·专题练习
名校
解题方法
5 . 已知函数f(x)=lnx﹣ax2﹣bx.
(1)当a=0时,f(x)有最大值﹣1,
(ⅰ)求实数b的值;
(ⅱ)证明:当x>1时,2lnx<(x﹣1)ex;
(2)a
时,f(x)存在两个极值点x1,x2(x2>x1)且f(x2)﹣f(x1)的取值范围是
,求b的取值范围.
(1)当a=0时,f(x)有最大值﹣1,
(ⅰ)求实数b的值;
(ⅱ)证明:当x>1时,2lnx<(x﹣1)ex;
(2)a
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a162dc68b1f6889351e5727b6d2d014e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb2c85531c49380d73f6b0f0d751d575.png)
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2021-09-29更新
|
1447次组卷
|
4卷引用:天津市武清区杨村一中2020-2021学年高二下学期期末数学试题
天津市武清区杨村一中2020-2021学年高二下学期期末数学试题天津市外国语大学附属外国语学校2021-2022学年高二下学期期中数学试题(已下线)专题3.5 利用导数研究函数的极值、最值-重难点题型精讲-2022年高考数学一轮复习举一反三系列(新高考地区专用)(已下线)第11讲 双变量不等式:极值和差商积问题-突破2022年新高考数学导数压轴解答题精选精练
6 . 已知椭圆
的左右焦点为
,
,
是椭圆上半部分的动点,连接
和长轴的左右两个端点所得两直线交
轴的正半轴于A,
两点
点A在
的上方或重合
.
(1)当
时,若B是线段OA的中点,求直线MA的方程;
(2)当
面积
最大时,求椭圆的方程;
(3)当
时,在
轴上是否存在点
使得
为定值,若存在,求
点的坐标,若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b1a5780b14053aa30c357d1316b4840.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd995178601c2ad7b40f973d268c7bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b71812e0762c0aaffb51cfef66156567.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b42fc33bcfc63ec2f4940ccd3f862400.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d73a483bf16151a9de6c6e651fa22f9b.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a3c442579603164f3fc19458677d307.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbad2b0ee693c245dcb51041dd07942b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
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7 . 已知椭圆C:
的焦距为
,其短轴的两个端点与长轴的一个端点构成正三角形.
(1)求椭圆C的方程;
(2)过点
且不过点
的直线与椭圆C交于A,B两点,直线AE与直线
交于点M.试判断直线BM与直线DE的位置关系,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bacae35b6e16a0a33c2bdc6bc07df7.png)
(1)求椭圆C的方程;
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d776a89f4fd29dccffe1040069d59ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e4c60a39479f30736dde0c6085833b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e55aa0a20848c37c1892c567b2315e04.png)
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名校
解题方法
8 . 已知椭圆
的长轴长为4,离心率为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/521e42b220eaac30bce6102bd8642104.png)
(1)求椭圆
的方程;
(2)设椭圆
的左焦点为F,右顶点为G,过点G的直线与y轴正半轴交于点S,与椭圆交于点H,且
轴,过点S的另一直线与椭圆交于M,N两点,若
,求直线MN的方程.
(3)圆锥曲线问题的关键一步是条件的翻译,所以请同学们不用解答,翻译下面的条件,转化为数学表达式:
①若直线
与双曲线
交于A、B两点,与其渐近线交于C、D两点,求证:AC=BD.
②椭圆的
左顶点为D,上顶点为B,点A的坐标为
,过点D的直线L与椭圆在第一象限交于点P,与直线AB交于点Q,设L的斜率为K,若
,求斜率K的值.
③椭圆的
左顶点为A,过点A作直线
与椭圆交于另一点B,若直线
交
轴于点C,且
,求直线
的斜率.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/521e42b220eaac30bce6102bd8642104.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7397bd90109ca5ab71e864cf91d58e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4146f877dfe6ca64f603ba1740850195.png)
(3)圆锥曲线问题的关键一步是条件的翻译,所以请同学们不用解答,翻译下面的条件,转化为数学表达式:
①若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae96f5020aef5aef03ec7f406460f608.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5ec7fa23be9cbe9a50607ea6bc8a4ff.png)
②椭圆的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c82e7d9f4f7ace849e09e9adcb786b7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff32d26c8d44f5fb4813a19c1030a9f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8172214950a628918b4d51fc6b24697.png)
③椭圆的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c82e7d9f4f7ace849e09e9adcb786b7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83ff26eeabfaef6e944082999e39e814.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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9 . 已知椭圆
,
分别为左右焦点,O为坐标原点,过O作直线
交椭圆于C,D两点,若
周长的最小值为6,面积的最大值为
.
(1)求椭圆E的方程;
(2)设直线
交椭圆E于A,B两点,
①若直线
的斜率为
且
的面积为
,求直线方程;
②若直线
与x轴交于M点,当点A在x轴的上方时,有
,且直线
与圆
相切于点N,求
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7e5578ca83f5bd5c285994061b9c015.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbdbb45d7359537458736c9ea5bf9e1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
(1)求椭圆E的方程;
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
①若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24c14ff9b66f21c05e52dc3c8908c2df.png)
②若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78b661c79b7b866204fd4084c37bdd4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41b658cce32a1d23f670aa479d49c0fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac35b1e8a952aac4f4cdaaf02d868d04.png)
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10 . 1.已知函数
,证明:当
时,
.
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2021-11-04更新
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8卷引用:天津市河东区2022-2023学年高二下学期期中模拟数学试题